Adversarial training deep neural networks often experience serious overfitting problem. Recently, it is explained that the overfitting happens because the sample complexity of training data is insufficient to generalize robustness. In traditional machine learning, one way to relieve overfitting from the lack of data is to use ensemble methods. However, adversarial training multiple networks is extremely expensive. Moreover, we found that there is a dilemma on choosing target model to generate adversarial examples. Optimizing attack to the members of ensemble will be suboptimal attack to the ensemble and incurs covariate shift, while attack to ensemble will weaken the members and lose the benefit from ensembling. In this paper, we propose adversarial training with Stochastic weight average (SWA); while performing adversarial training, we aggregate the temporal weight states in the trajectory of training. By adopting SWA, the benefit of ensemble can be gained without tremendous computational increment and without facing the dilemma. Moreover, we further improved SWA to be adequate to adversarial training. The empirical results on CIFAR-10, CIFAR-100 and SVHN show that our method can improve the robustness of models.
View on arXiv